$A$ coin is tossed three times. Let $A$ be the event of "getting three heads" and $B$ be the event of "getting a head on the first toss". Then $A$ and $B$ are

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

Two dice are thrown. The events $A$,$B$,and $C$ are as follows:
$A$: getting an even number on the first die.
$B$: getting an odd number on the first die.
$C$: getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive.

If $A, B, C$ are three events of a sample space such that $P(B)=\frac{3}{2} P(A)$ and $P(C)=\frac{1}{2} P(B)$,then which of the following is correct?

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is